1/18x+2/3=5/6x

Solution for 1/18x+2/3=5/6x equation:

1/18x+2/3=5/6x

We move all terms to the left:

1/18x+2/3-(5/6x)=0


Domain of the equation: 18x!=0

x!=0/18

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/18x-(+5/6x)+2/3=0

We get rid of parentheses

1/18x-5/6x+2/3=0

We calculate fractions


1296x^2/972x^2+54x/972x^2+(-810x)/972x^2=0

We multiply all the terms by the denominator


1296x^2+54x+(-810x)=0

We get rid of parentheses

1296x^2+54x-810x=0

We add all the numbers together, and all the variables

1296x^2-756x=0

a = 1296; b = -756; c = 0;
Δ = b2-4ac
Δ = -7562-4·1296·0
Δ = 571536
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{571536}=756$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-756)-756}{2*1296}=\frac{0}{2592}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-756)+756}{2*1296}=\frac{1512}{2592}
=7/12
$